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Similarity profiles of flows through porous media. (English) Zbl 0249.35043


MSC:

35K10 Second-order parabolic equations
35K15 Initial value problems for second-order parabolic equations
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[1] Craven, A. H., & L. A. Peletier, Similarity solutions for degenerate quasi-linear parabolic equations. J. Math. Anal. and Appl. (to appear). · Zbl 0237.35043
[2] Dunford, N., & J. T. Schwartz, Linear Operators I, p. 459. New York: Interscience Publishers, 1958.
[3] Hartman, P., Ordinary Differential Equations. New York: Wiley 1964. · Zbl 0125.32102
[4] Muskat, M., The Flow of Homogeneous Fluids Through Porous Media. New York: McGraw-Hill, 1937. · JFM 63.1368.03
[5] Oleinik, O. A., A. S. Kalashnikov, & Chzhou Yui-Lin, The Cauchy problem and boundary problems for equations of the type of nonstationary filtration. Izv. Akad. Nauk. SSSR, Ser. Mat. 22, 667–704 (1958).
[6] Peletder, L. A., Asymptotic behaviour of temperature profiles of a class of non-linear heat conduction problems. Quart. J. Mech. and Appl. Math. 23, 441–447 (1970). · Zbl 0203.41003
[7] Peletier, L. A., Asymptotic behaviour of solutions of the porous media equation. SIAM J. Applied Math. (to appear). · Zbl 0229.35010
[8] Serrin, J., Asymptotic behaviour of velocity profiles in the Prandtl boundary layer theory. Proc. Roy. Soc. A299, 491–507 (1967). · Zbl 0149.44901
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